| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 36.0.116...569.1 |
$x^{36} - x^{35} + x^{33} - x^{32} + x^{30} - x^{29} + x^{27} - x^{26} + x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{16} + x^{15} - x^{13} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 19^{34}$ |
$2$ |
$27.9429569456$ |
$27.942956945645935$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[9]$ |
$114$ |
$17$ |
$719116485989.9799$ |
| 36.0.599...464.1 |
$x^{36} - x^{18} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}$ |
$2$ |
$31.1769145362$ |
$31.176914536239792$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$108$ |
$17$ |
$2861978396449.9033$ |
| 36.0.206...656.1 |
$x^{36} - x^{34} + x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 19^{34}$ |
$2$ |
$32.265747429$ |
$32.26574742904561$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$76$ |
$17$ |
$2595333985839.583$ |
| 36.0.332...625.1 |
$x^{36} - 76 x^{27} + 5777 x^{18} + 76 x^{9} + 1$ |
$36$ |
[0,18] |
$3^{90}\cdot 5^{18}$ |
$2$ |
$34.8568501159$ |
$34.85685011586675$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[37]$ |
$54$ |
$17$ |
$6550249244897.024$ |
| 36.0.114...625.1 |
$x^{36} - x^{35} + 2 x^{34} - 3 x^{33} + 5 x^{32} - 8 x^{31} + 13 x^{30} - 21 x^{29} + 34 x^{28} - 55 x^{27} + 89 x^{26} - 144 x^{25} + 233 x^{24} - 377 x^{23} + 610 x^{22} - 987 x^{21} + 1597 x^{20} - 2584 x^{19} + 4181 x^{18} + 2584 x^{17} + 1597 x^{16} + 987 x^{15} + 610 x^{14} + 377 x^{13} + 233 x^{12} + 144 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$36$ |
[0,18] |
$5^{18}\cdot 19^{34}$ |
$2$ |
$36.0742022981$ |
$36.07420229809253$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[76]$ |
$38$ |
$17$ |
$3431432369157.3267$ |
| 36.0.142...601.1 |
$x^{36} - 5 x^{27} - 487 x^{18} - 2560 x^{9} + 262144$ |
$36$ |
[0,18] |
$3^{90}\cdot 7^{18}$ |
$2$ |
$41.2431812546$ |
$41.24318125460256$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.489...729.1 |
$x^{36} - x^{35} - x^{34} + 3 x^{33} - x^{32} - 5 x^{31} + 7 x^{30} + 3 x^{29} - 17 x^{28} + 11 x^{27} + 23 x^{26} - 45 x^{25} - x^{24} + 91 x^{23} - 89 x^{22} - 93 x^{21} + 271 x^{20} - 85 x^{19} - 457 x^{18} - 170 x^{17} + 1084 x^{16} - 744 x^{15} - 1424 x^{14} + 2912 x^{13} - 64 x^{12} - 5760 x^{11} + 5888 x^{10} + 5632 x^{9} - 17408 x^{8} + 6144 x^{7} + 28672 x^{6} - 40960 x^{5} - 16384 x^{4} + 98304 x^{3} - 65536 x^{2} - 131072 x + 262144$ |
$36$ |
[0,18] |
$7^{18}\cdot 19^{34}$ |
$2$ |
$42.6835717814$ |
$42.68357178143818$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[2, 74]$ |
$38$ |
$17$ |
$28076820524481.113$ |
| 36.0.157...816.1 |
$x^{36} - 512 x^{18} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
$44.090815370097204$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.157...816.2 |
$x^{36} + 512 x^{18} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
$44.090815370097204$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.541...464.1 |
$x^{36} - 2 x^{34} + 4 x^{32} - 8 x^{30} + 16 x^{28} - 32 x^{26} + 64 x^{24} - 128 x^{22} + 256 x^{20} - 512 x^{18} + 1024 x^{16} - 2048 x^{14} + 4096 x^{12} - 8192 x^{10} + 16384 x^{8} - 32768 x^{6} + 65536 x^{4} - 131072 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
$45.630657614261125$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.541...464.2 |
$x^{36} + 2 x^{34} + 4 x^{32} + 8 x^{30} + 16 x^{28} + 32 x^{26} + 64 x^{24} + 128 x^{22} + 256 x^{20} + 512 x^{18} + 1024 x^{16} + 2048 x^{14} + 4096 x^{12} + 8192 x^{10} + 16384 x^{8} + 32768 x^{6} + 65536 x^{4} + 131072 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
$45.630657614261125$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.221...944.1 |
$x^{36} - 17 x^{34} + 169 x^{32} - 1130 x^{30} + 5664 x^{28} - 21853 x^{26} + 66874 x^{24} - 162613 x^{22} + 316711 x^{20} - 487810 x^{18} + 592078 x^{16} - 549123 x^{14} + 384931 x^{12} - 190091 x^{10} + 66033 x^{8} - 13002 x^{6} + 1695 x^{4} - 45 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{32}$ |
$3$ |
$47.4526521699$ |
$47.4526521699425$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[171]$ |
$12$ |
$17$ |
$119587984215961.08$ |
| 36.0.485...969.1 |
$x^{36} - 136 x^{27} - 1187 x^{18} - 2676888 x^{9} + 387420489$ |
$36$ |
[0,18] |
$3^{90}\cdot 11^{18}$ |
$2$ |
$51.7010638188$ |
$51.70106381884226$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.807...721.1 |
$x^{36} - x^{35} + 18 x^{34} - 15 x^{33} + 185 x^{32} - 137 x^{31} + 1281 x^{30} - 831 x^{29} + 6616 x^{28} - 3799 x^{27} + 26339 x^{26} - 13196 x^{25} + 83006 x^{24} - 36260 x^{23} + 208286 x^{22} - 77735 x^{21} + 418163 x^{20} - 132518 x^{19} + 666068 x^{18} - 173318 x^{17} + 834766 x^{16} - 177139 x^{15} + 804267 x^{14} - 129870 x^{13} + 582511 x^{12} - 73129 x^{11} + 302060 x^{10} - 23507 x^{9} + 107217 x^{8} - 7128 x^{7} + 23244 x^{6} - 78 x^{5} + 2775 x^{4} - 165 x^{3} + 126 x^{2} + 9 x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 37^{34}$ |
$2$ |
$52.4372651879$ |
$52.43726518793858$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[19, 684]$ |
$6$ |
$17$ |
$3171872728760.222$ |
| 36.0.122...625.1 |
$x^{36} - x^{35} + 26 x^{34} - 15 x^{33} + 413 x^{32} - 173 x^{31} + 4027 x^{30} - 789 x^{29} + 28017 x^{28} - 2298 x^{27} + 134511 x^{26} + 7347 x^{25} + 472642 x^{24} + 48836 x^{23} + 1180619 x^{22} + 171615 x^{21} + 2210278 x^{20} + 335012 x^{19} + 3064502 x^{18} + 471070 x^{17} + 3227734 x^{16} + 424487 x^{15} + 2498777 x^{14} + 259210 x^{13} + 1437594 x^{12} + 75846 x^{11} + 567447 x^{10} - 2642 x^{9} + 158238 x^{8} - 9682 x^{7} + 24598 x^{6} - 3269 x^{5} + 2670 x^{4} - 215 x^{3} + 80 x^{2} + 5 x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 5^{18}\cdot 19^{32}$ |
$3$ |
$53.0536779823$ |
$53.05367798232217$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[9, 1629]$ |
$6$ |
$17$ |
$3431432369157.3267$ |
| 36.0.166...801.1 |
$x^{36} - x^{35} - 2 x^{34} + 5 x^{33} + x^{32} - 16 x^{31} + 13 x^{30} + 35 x^{29} - 74 x^{28} - 31 x^{27} + 253 x^{26} - 160 x^{25} - 599 x^{24} + 1079 x^{23} + 718 x^{22} - 3955 x^{21} + 1801 x^{20} + 10064 x^{19} - 15467 x^{18} + 30192 x^{17} + 16209 x^{16} - 106785 x^{15} + 58158 x^{14} + 262197 x^{13} - 436671 x^{12} - 349920 x^{11} + 1659933 x^{10} - 610173 x^{9} - 4369626 x^{8} + 6200145 x^{7} + 6908733 x^{6} - 25509168 x^{5} + 4782969 x^{4} + 71744535 x^{3} - 86093442 x^{2} - 129140163 x + 387420489$ |
$36$ |
[0,18] |
$11^{18}\cdot 19^{34}$ |
$2$ |
$53.5066889013$ |
$53.50668890125934$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.392...656.1 |
$x^{36} + 49 x^{32} + 932 x^{28} + 8695 x^{24} + 41461 x^{20} + 96055 x^{16} + 93536 x^{12} + 28314 x^{8} + 1365 x^{4} + 1$ |
$36$ |
[0,18] |
$2^{72}\cdot 19^{32}$ |
$2$ |
$54.7936030082$ |
$54.79360300815596$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[19, 171]$ |
$8$ |
$17$ |
$28122649019657.055$ |
| 36.0.799...784.1 |
$x^{36} + 37 x^{34} + 628 x^{32} + 6478 x^{30} + 45354 x^{28} + 227942 x^{26} + 848161 x^{24} + 2375189 x^{22} + 5038516 x^{20} + 8084594 x^{18} + 9725341 x^{16} + 8624289 x^{14} + 5490811 x^{12} + 2413645 x^{10} + 691677 x^{8} + 118407 x^{6} + 10470 x^{4} + 360 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{34}$ |
$3$ |
$55.8859138913$ |
$55.88591389129187$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[52934]$ |
$4$ |
$17$ |
$1438232971979.9597$ |
| 36.36.799...784.1 |
$x^{36} - 35 x^{34} + 560 x^{32} - 5426 x^{30} + 35554 x^{28} - 166634 x^{26} + 576201 x^{24} - 1494747 x^{22} + 2929464 x^{20} - 4334718 x^{18} + 4805781 x^{16} - 3932287 x^{14} + 2318239 x^{12} - 949739 x^{10} + 256105 x^{8} - 41769 x^{6} + 3570 x^{4} - 120 x^{2} + 1$ |
$36$ |
[36,0] |
$2^{36}\cdot 3^{18}\cdot 19^{34}$ |
$3$ |
$55.8859138913$ |
$55.88591389129187$ |
|
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$104443369202940970000$ |
| 36.0.799...784.2 |
$x^{36} + 19 x^{34} + 209 x^{32} + 1558 x^{30} + 8740 x^{28} + 38095 x^{26} + 132810 x^{24} + 372723 x^{22} + 848787 x^{20} + 1558038 x^{18} + 2298126 x^{16} + 2670317 x^{14} + 2415451 x^{12} + 1629193 x^{10} + 806113 x^{8} + 262086 x^{6} + 57399 x^{4} + 5415 x^{2} + 361$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{34}$ |
$3$ |
$55.8859138913$ |
$55.88591389129187$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$6$ |
$17$ |
|
| 36.0.799...784.3 |
$x^{36} + 3 x^{34} + 9 x^{32} + 27 x^{30} + 81 x^{28} + 243 x^{26} + 729 x^{24} + 2187 x^{22} + 6561 x^{20} + 19683 x^{18} + 59049 x^{16} + 177147 x^{14} + 531441 x^{12} + 1594323 x^{10} + 4782969 x^{8} + 14348907 x^{6} + 43046721 x^{4} + 129140163 x^{2} + 387420489$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{34}$ |
$3$ |
$55.8859138913$ |
$55.88591389129187$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.981...921.1 |
$x^{36} - 1810 x^{27} + 3295783 x^{18} + 35626230 x^{9} + 387420489$ |
$36$ |
[0,18] |
$3^{90}\cdot 13^{18}$ |
$2$ |
$56.2049819856$ |
$56.20498198558558$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.337...009.1 |
$x^{36} - x^{35} + 4 x^{34} - 7 x^{33} + 19 x^{32} - 40 x^{31} + 97 x^{30} - 217 x^{29} + 508 x^{28} - 1159 x^{27} + 2683 x^{26} - 6160 x^{25} + 14209 x^{24} - 32689 x^{23} + 75316 x^{22} - 173383 x^{21} + 399331 x^{20} - 919480 x^{19} + 2117473 x^{18} + 2758440 x^{17} + 3593979 x^{16} + 4681341 x^{15} + 6100596 x^{14} + 7943427 x^{13} + 10358361 x^{12} + 13471920 x^{11} + 17603163 x^{10} + 22812597 x^{9} + 29996892 x^{8} + 38440899 x^{7} + 51549777 x^{6} + 63772920 x^{5} + 90876411 x^{4} + 100442349 x^{3} + 172186884 x^{2} + 129140163 x + 387420489$ |
$36$ |
[0,18] |
$13^{18}\cdot 19^{34}$ |
$2$ |
$58.1679033983$ |
$58.16790339829716$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.457...056.1 |
$x^{36} + 54 x^{32} + 1143 x^{28} + 12006 x^{24} + 65367 x^{20} + 175806 x^{16} + 203838 x^{12} + 70632 x^{8} + 5481 x^{4} + 1$ |
$36$ |
[0,18] |
$2^{72}\cdot 3^{88}$ |
$2$ |
$58.6619359999$ |
$58.661935999878466$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[6327]$ |
$8$ |
$17$ |
$44130898078069.0$ |
| 36.0.143...304.1 |
$x^{36} + 35 x^{34} + 561 x^{32} + 5456 x^{30} + 35960 x^{28} + 169911 x^{26} + 593775 x^{24} + 1560780 x^{22} + 3108105 x^{20} + 4686825 x^{18} + 5311735 x^{16} + 4457400 x^{14} + 2704156 x^{12} + 1144066 x^{10} + 319770 x^{8} + 54264 x^{6} + 4845 x^{4} + 171 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 37^{34}$ |
$2$ |
$60.5493383436$ |
$60.54933834364826$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[130473]$ |
$4$ |
$17$ |
$3171872728760.222$ |
| 36.0.218...000.1 |
$x^{36} + 51 x^{34} + 1129 x^{32} + 14310 x^{30} + 115592 x^{28} + 628407 x^{26} + 2373706 x^{24} + 6356559 x^{22} + 12218191 x^{20} + 16953894 x^{18} + 16964206 x^{16} + 12133089 x^{14} + 6090371 x^{12} + 2080353 x^{10} + 460449 x^{8} + 61182 x^{6} + 4335 x^{4} + 135 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 5^{18}\cdot 19^{32}$ |
$3$ |
$61.2611105292$ |
$61.26111052918685$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[81529]$ |
$4$ |
$17$ |
$3431432369157.3267$ |
| 36.36.412...504.1 |
$x^{36} - 36 x^{34} + 594 x^{32} - 5952 x^{30} + 40455 x^{28} - 197316 x^{26} + 712530 x^{24} - 1937520 x^{22} + 3996135 x^{20} - 6249100 x^{18} + 7354710 x^{16} - 6418656 x^{14} + 4056234 x^{12} - 1790712 x^{10} + 523260 x^{8} - 93024 x^{6} + 8721 x^{4} - 324 x^{2} + 1$ |
$36$ |
[36,0] |
$2^{72}\cdot 3^{90}$ |
$2$ |
$62.3538290725$ |
$62.353829072479584$ |
|
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$682049432255791000000$ |
| 36.0.412...504.1 |
$x^{36} + 36 x^{34} + 594 x^{32} + 5952 x^{30} + 40455 x^{28} + 197316 x^{26} + 712530 x^{24} + 1937520 x^{22} + 3996135 x^{20} + 6249100 x^{18} + 7354710 x^{16} + 6418656 x^{14} + 4056234 x^{12} + 1790712 x^{10} + 523260 x^{8} + 93024 x^{6} + 8721 x^{4} + 324 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{72}\cdot 3^{90}$ |
$2$ |
$62.3538290725$ |
$62.353829072479584$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[180486]$ |
$2$ |
$17$ |
$2861978396449.9033$ |
| 36.0.412...504.2 |
$x^{36} + 54 x^{32} + 1143 x^{28} + 12006 x^{24} + 65367 x^{20} + 175878 x^{16} + 201654 x^{12} + 77760 x^{8} + 3321 x^{4} + 9$ |
$36$ |
[0,18] |
$2^{72}\cdot 3^{90}$ |
$2$ |
$62.3538290725$ |
$62.353829072479584$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[10298]$ |
$4$ |
$17$ |
$77725882445830.34$ |
| 36.36.443...625.1 |
$x^{36} - x^{35} - 55 x^{34} + 54 x^{33} + 1316 x^{32} - 1262 x^{31} - 18056 x^{30} + 16794 x^{29} + 157962 x^{28} - 141168 x^{27} - 929619 x^{26} + 788451 x^{25} + 3797668 x^{24} - 3009217 x^{23} - 10994500 x^{22} + 7985283 x^{21} + 22875412 x^{20} - 14890129 x^{19} - 34467709 x^{18} + 19586929 x^{17} + 37621312 x^{16} - 18102232 x^{15} - 29492311 x^{14} + 11597407 x^{13} + 16278597 x^{12} - 5027655 x^{11} - 6107727 x^{10} + 1424143 x^{9} + 1470387 x^{8} - 252736 x^{7} - 206783 x^{6} + 26779 x^{5} + 14445 x^{4} - 1460 x^{3} - 340 x^{2} + 20 x + 1$ |
$36$ |
[36,0] |
$3^{18}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$62.4823512228$ |
$62.48235122281421$ |
|
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$736998020653083800000$ |
| 36.0.443...625.1 |
$x^{36} - x^{35} + 35 x^{34} - 31 x^{33} + 556 x^{32} - 432 x^{31} + 5314 x^{30} - 3586 x^{29} + 34162 x^{28} - 19818 x^{27} + 156466 x^{26} - 77194 x^{25} + 527433 x^{24} - 218657 x^{23} + 1332275 x^{22} - 457647 x^{21} + 2542252 x^{20} - 711664 x^{19} + 3665766 x^{18} - 809761 x^{17} + 3956632 x^{16} - 539957 x^{15} + 3063059 x^{14} + 517817 x^{13} + 1345047 x^{12} + 2800770 x^{11} - 276502 x^{10} + 5237843 x^{9} - 1026513 x^{8} + 5476374 x^{7} - 560238 x^{6} + 2102034 x^{5} + 267795 x^{4} + 3047715 x^{3} - 4108065 x^{2} - 5418330 x + 21850951$ |
$36$ |
[0,18] |
$3^{18}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$62.4823512228$ |
$62.48235122281421$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[247608]$ |
$2$ |
$17$ |
$1438232971979.9597$ |
| 36.0.443...625.2 |
$x^{36} - x^{35} - 19 x^{34} + 20 x^{33} + 208 x^{32} - 228 x^{31} - 1538 x^{30} + 1766 x^{29} + 8512 x^{28} - 10278 x^{27} - 36329 x^{26} + 46607 x^{25} + 122532 x^{24} - 169139 x^{23} - 326116 x^{22} + 495255 x^{21} + 679648 x^{20} - 1174903 x^{19} - 1062783 x^{18} + 2247035 x^{17} + 1113874 x^{16} - 3183278 x^{15} - 600913 x^{14} + 942095 x^{13} + 2074269 x^{12} + 3200721 x^{11} - 6904183 x^{10} + 19867883 x^{9} - 12157587 x^{8} - 58512762 x^{7} + 70408263 x^{6} + 11551791 x^{5} - 81902655 x^{4} + 82074510 x^{3} - 177270 x^{2} - 87226170 x + 87403801$ |
$36$ |
[0,18] |
$3^{18}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$62.4823512228$ |
$62.48235122281421$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$6$ |
$17$ |
|
| 36.0.443...625.3 |
$x^{36} - x^{35} - 3 x^{34} + 7 x^{33} + 5 x^{32} - 33 x^{31} + 13 x^{30} + 119 x^{29} - 171 x^{28} - 305 x^{27} + 989 x^{26} + 231 x^{25} - 4187 x^{24} + 3263 x^{23} + 13485 x^{22} - 26537 x^{21} - 27403 x^{20} + 133551 x^{19} - 23939 x^{18} + 534204 x^{17} - 438448 x^{16} - 1698368 x^{15} + 3452160 x^{14} + 3341312 x^{13} - 17149952 x^{12} + 3784704 x^{11} + 64815104 x^{10} - 79953920 x^{9} - 179306496 x^{8} + 499122176 x^{7} + 218103808 x^{6} - 2214592512 x^{5} + 1342177280 x^{4} + 7516192768 x^{3} - 12884901888 x^{2} - 17179869184 x + 68719476736$ |
$36$ |
[0,18] |
$3^{18}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$62.4823512228$ |
$62.48235122281421$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.524...921.1 |
$x^{36} - x^{35} - 25 x^{34} + 12 x^{33} + 338 x^{32} - 35 x^{31} - 3596 x^{30} + 75 x^{29} + 31599 x^{28} + 708 x^{27} - 221058 x^{26} - 33939 x^{25} + 1281217 x^{24} + 260669 x^{23} - 6307141 x^{22} - 1034028 x^{21} + 25482307 x^{20} + 5036015 x^{19} - 82683121 x^{18} - 21277922 x^{17} + 219610804 x^{16} + 36478832 x^{15} - 460870720 x^{14} - 25242848 x^{13} + 716973312 x^{12} + 105430656 x^{11} - 784816896 x^{10} - 223400960 x^{9} + 631394304 x^{8} + 37050368 x^{7} - 296185856 x^{6} + 80846848 x^{5} + 88227840 x^{4} - 13107200 x^{3} - 3604480 x^{2} - 655360 x + 262144$ |
$36$ |
[0,18] |
$3^{18}\cdot 7^{18}\cdot 19^{32}$ |
$3$ |
$62.7739583461$ |
$62.773958346058684$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[2, 666]$ |
$6$ |
$17$ |
$1513299055779282.5$ |
| 36.0.122...041.1 |
$x^{36} - 4693 x^{27} + 22286393 x^{18} + 1230241792 x^{9} + 68719476736$ |
$36$ |
[0,18] |
$3^{90}\cdot 17^{18}$ |
$2$ |
$64.2728558569$ |
$64.27285585688566$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.141...816.1 |
$x^{36} + 36 x^{34} + 593 x^{32} + 5920 x^{30} + 39992 x^{28} + 193312 x^{26} + 689479 x^{24} + 1844392 x^{22} + 3724921 x^{20} + 5673268 x^{18} + 6463399 x^{16} + 5422832 x^{14} + 3269436 x^{12} + 1365584 x^{10} + 374154 x^{8} + 61776 x^{6} + 5325 x^{4} + 180 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{72}\cdot 19^{34}$ |
$2$ |
$64.5314948581$ |
$64.53149485809122$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[171, 1026]$ |
$2$ |
$17$ |
$2595333985839.583$ |
| 36.36.141...816.1 |
$x^{36} - 36 x^{34} + 593 x^{32} - 5920 x^{30} + 39992 x^{28} - 193312 x^{26} + 689479 x^{24} - 1844392 x^{22} + 3724921 x^{20} - 5673268 x^{18} + 6463399 x^{16} - 5422832 x^{14} + 3269436 x^{12} - 1365584 x^{10} + 374154 x^{8} - 61776 x^{6} + 5325 x^{4} - 180 x^{2} + 1$ |
$36$ |
[36,0] |
$2^{72}\cdot 19^{34}$ |
$2$ |
$64.5314948581$ |
$64.53149485809122$ |
|
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$1426609831093226200000$ |
| 36.0.141...816.2 |
$x^{36} + 57 x^{32} + 1292 x^{28} + 14839 x^{24} + 91181 x^{20} + 291327 x^{16} + 436088 x^{12} + 246202 x^{8} + 33573 x^{4} + 361$ |
$36$ |
[0,18] |
$2^{72}\cdot 19^{34}$ |
$2$ |
$64.5314948581$ |
$64.53149485809122$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[19, 1026]$ |
$4$ |
$17$ |
$83538158776577.44$ |
| 36.0.254...000.1 |
$x^{36} + 54 x^{34} + 1269 x^{32} + 17118 x^{30} + 147510 x^{28} + 857304 x^{26} + 3468195 x^{24} + 9962190 x^{22} + 20569950 x^{20} + 30703482 x^{18} + 33080274 x^{16} + 25472799 x^{14} + 13732377 x^{12} + 5001777 x^{10} + 1161216 x^{8} + 156168 x^{6} + 10341 x^{4} + 243 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{88}\cdot 5^{18}$ |
$3$ |
$65.5860382937$ |
$65.58603829373517$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[19, 12483]$ |
$4$ |
$17$ |
$6550249244897.024$ |
| 36.0.422...489.1 |
$x^{36} - x^{35} + 5 x^{34} - 9 x^{33} + 29 x^{32} - 65 x^{31} + 181 x^{30} - 441 x^{29} + 1165 x^{28} - 2929 x^{27} + 7589 x^{26} - 19305 x^{25} + 49661 x^{24} - 126881 x^{23} + 325525 x^{22} - 833049 x^{21} + 2135149 x^{20} - 5467345 x^{19} + 14007941 x^{18} + 21869380 x^{17} + 34162384 x^{16} + 53315136 x^{15} + 83334400 x^{14} + 129926144 x^{13} + 203411456 x^{12} + 316293120 x^{11} + 497352704 x^{10} + 767819776 x^{9} + 1221591040 x^{8} + 1849688064 x^{7} + 3036676096 x^{6} + 4362076160 x^{5} + 7784628224 x^{4} + 9663676416 x^{3} + 21474836480 x^{2} + 17179869184 x + 68719476736$ |
$36$ |
[0,18] |
$17^{18}\cdot 19^{34}$ |
$2$ |
$66.5175423697$ |
$66.51754236972826$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.580...936.1 |
$x^{36} - 34 x^{34} + 676 x^{32} - 9040 x^{30} + 90624 x^{28} - 699296 x^{26} + 4279936 x^{24} - 20814464 x^{22} + 81078016 x^{20} - 249758720 x^{18} + 606287872 x^{16} - 1124603904 x^{14} + 1576677376 x^{12} - 1557225472 x^{10} + 1081884672 x^{8} - 426049536 x^{6} + 111083520 x^{4} - 5898240 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{18}\cdot 19^{32}$ |
$3$ |
$67.1081842693$ |
$67.10818426930577$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$6$ |
$17$ |
|
| 36.0.580...936.2 |
$x^{36} + 34 x^{34} + 676 x^{32} + 9040 x^{30} + 90624 x^{28} + 699296 x^{26} + 4279936 x^{24} + 20814464 x^{22} + 81078016 x^{20} + 249758720 x^{18} + 606287872 x^{16} + 1124603904 x^{14} + 1576677376 x^{12} + 1557225472 x^{10} + 1081884672 x^{8} + 426049536 x^{6} + 111083520 x^{4} + 5898240 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{18}\cdot 19^{32}$ |
$3$ |
$67.1081842693$ |
$67.10818426930577$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$6$ |
$17$ |
|
| 36.36.794...625.1 |
$x^{36} - x^{35} - 52 x^{34} + 47 x^{33} + 1177 x^{32} - 947 x^{31} - 15301 x^{30} + 10771 x^{29} + 127184 x^{28} - 76859 x^{27} - 713805 x^{26} + 363060 x^{25} + 2791702 x^{24} - 1171922 x^{23} - 7758928 x^{22} + 2637723 x^{21} + 15506227 x^{20} - 4188542 x^{19} - 22401208 x^{18} + 4709558 x^{17} + 23361262 x^{16} - 3730447 x^{15} - 17429913 x^{14} + 2049918 x^{13} + 9135431 x^{12} - 759461 x^{11} - 3261522 x^{10} + 180587 x^{9} + 755073 x^{8} - 24948 x^{7} - 104688 x^{6} + 1398 x^{5} + 7575 x^{4} + 75 x^{3} - 216 x^{2} - 9 x + 1$ |
$36$ |
[36,0] |
$5^{18}\cdot 37^{34}$ |
$2$ |
$67.6962182645$ |
$67.69621826451602$ |
|
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$2894219484422715000000$ |
| 36.0.908...609.1 |
$x^{36} - 2506 x^{27} + 4326911 x^{18} - 4894531250 x^{9} + 3814697265625$ |
$36$ |
[0,18] |
$3^{90}\cdot 19^{18}$ |
$2$ |
$67.9485099174$ |
$67.94850991743675$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.36.228...000.1 |
$x^{36} - 54 x^{34} + 1269 x^{32} - 17118 x^{30} + 147510 x^{28} - 857304 x^{26} + 3468195 x^{24} - 9962190 x^{22} + 20569950 x^{20} - 30715038 x^{18} + 33159726 x^{16} - 25700409 x^{14} + 14084001 x^{12} - 5318379 x^{10} + 1328724 x^{8} - 206064 x^{6} + 17901 x^{4} - 729 x^{2} + 9$ |
$36$ |
[36,0] |
$2^{36}\cdot 3^{90}\cdot 5^{18}$ |
$3$ |
$69.7137002317$ |
$69.7137002317335$ |
|
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$6642656411972985000000$ |
| 36.0.228...000.1 |
$x^{36} - 1953125 x^{18} + 3814697265625$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}\cdot 5^{18}$ |
$3$ |
$69.7137002317$ |
$69.7137002317335$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.228...000.2 |
$x^{36} + 36 x^{34} + 594 x^{32} + 5952 x^{30} + 40455 x^{28} + 197316 x^{26} + 712530 x^{24} + 1937520 x^{22} + 3996135 x^{20} + 6243322 x^{18} + 7250706 x^{16} + 5638626 x^{14} + 901446 x^{12} - 5645574 x^{10} - 9773136 x^{8} - 7915284 x^{6} - 3111399 x^{4} - 467694 x^{2} + 33373729$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}\cdot 5^{18}$ |
$3$ |
$69.7137002317$ |
$69.7137002317335$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[923742]$ |
$2$ |
$17$ |
$5723956792899.807$ |
| 36.0.228...000.3 |
$x^{36} - 36 x^{34} + 594 x^{32} - 5952 x^{30} + 40455 x^{28} - 197316 x^{26} + 712530 x^{24} - 1937520 x^{22} + 3996135 x^{20} - 6254878 x^{18} + 7458714 x^{16} - 7198686 x^{14} + 7211022 x^{12} - 9226998 x^{10} + 10819656 x^{8} - 8101332 x^{6} + 3128841 x^{4} - 468342 x^{2} + 33396841$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}\cdot 5^{18}$ |
$3$ |
$69.7137002317$ |
$69.7137002317335$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[1406]$ |
$4$ |
$17$ |
$5100074719720140.0$ |
| 36.36.787...000.1 |
$x^{36} - 57 x^{34} + 1425 x^{32} - 20634 x^{30} + 192812 x^{28} - 1228749 x^{26} + 5515738 x^{24} - 17801385 x^{22} + 41855195 x^{20} - 72233250 x^{18} + 91675950 x^{16} - 85215855 x^{14} + 57368315 x^{12} - 27413979 x^{10} + 9002257 x^{8} - 1929906 x^{6} + 248007 x^{4} - 16245 x^{2} + 361$ |
$36$ |
[36,0] |
$2^{36}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$72.1484045962$ |
$72.14840459618506$ |
|
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
trivial |
$2$ |
$35$ |
$12611979161433870000000$ |
| 36.0.787...000.1 |
$x^{36} - 5 x^{34} + 25 x^{32} - 125 x^{30} + 625 x^{28} - 3125 x^{26} + 15625 x^{24} - 78125 x^{22} + 390625 x^{20} - 1953125 x^{18} + 9765625 x^{16} - 48828125 x^{14} + 244140625 x^{12} - 1220703125 x^{10} + 6103515625 x^{8} - 30517578125 x^{6} + 152587890625 x^{4} - 762939453125 x^{2} + 3814697265625$ |
$36$ |
[0,18] |
$2^{36}\cdot 5^{18}\cdot 19^{34}$ |
$3$ |
$72.1484045962$ |
$72.14840459618506$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
